A368250 Decimal expansion of Sum_{k>=2} (zeta(k)/zeta(2*k) - 1).

8, 4, 8, 6, 3, 3, 8, 6, 7, 9, 6, 4, 8, 8, 3, 6, 3, 2, 6, 8, 4, 9, 0, 0, 1, 2, 0, 9, 0, 4, 3, 0, 4, 6, 2, 9, 6, 0, 0, 1, 6, 6, 4, 4, 6, 8, 8, 1, 7, 5, 5, 1, 7, 1, 6, 7, 9, 6, 2, 0, 3, 0, 9, 0, 0, 3, 6, 5, 4, 2, 2, 1, 3, 7, 1, 3, 0, 2, 1, 2, 9, 1, 8, 8, 6, 6, 3, 4, 8, 1, 0, 1, 1, 5, 3, 7, 0, 2, 0, 6, 3, 4, 4, 3, 7

Offset: 0

Author

Amiram Eldar, Dec 19 2023

Keywords

• nonn
• cons

Examples

			0.84863386796488363268490012090430462960016644688175...
		

Links

• Michael I. Shamos, Shamos's catalog of the real numbers, 2011. See p. 637.

Crossrefs

Cf. A008683, A072777, A368249, A368251.

Programs

Maple

evalf(sum(Zeta(k)/Zeta(2*k) - 1, k = 2 .. infinity), 120);

PARI

sumpos(k=2, zeta(k)/zeta(2*k) - 1)

Formula

Equals Sum_{k>=2} mu(k)^2/(k*(k-1)) = Sum_{k>=2} 1/A368249(k).

Equals Sum_{k>=1} 1/A072777(k).

Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A368251(k).